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Bundeswettbewerb Mathematik 1981 Problem 2.1

Source: Bundeswettbewerb Mathematik 1981 Round 2

September 22, 2022
floor functionSequenceoddalgebra

Problem Statement

A sequence a1,a2,a3,…a_1, a_2, a_3, \ldots is defined as follows: a1a_1 is a positive integer and an+1=⌊32an⌋+1a_{n+1} = \left\lfloor \frac{3}{2} a_n \right\rfloor +1 for all n∈Nn \in \mathbb{N}. Can a1a_1 be chosen in such a way that the first 100000100000 terms of the sequence are even, but the 100001100001-th term is odd?
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